Estimating the Effective Reproduction Number of COVID-19 in South Africa
Louis Rossouw
2021-04-23 21:30:02
1 Introduction
This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various provinces \(m\) of South Africa. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was b141aff519ee125929b3b6f686b1070f3fc70742.
A major recent update made on 29 March 2021 was to switch from data based on cases reported as captured in [3] to a data source that contains cases by date the specimen was received [4].
A further update on 17 April 2021 was to adjust cases for public holidays and on 18 April 2021 basic testing data was also added.
2 Data
2.1 Data Source
Case data is extracted from the NICD National COVID-19 Daily Report [4]. This contains the daily cases reported by the NICD for South Africa by province. Data is shown by specimen reported date. Most recent data is excluded due to incomplete reporting of tests in last number of days.
This report contains data as released at 2021-04-23 21:01:06.
2.2 Data Fixes
The following fixes are applied:
- Calculate daily new cases from cumulative data captured.
- Add a total for South Africa as a whole.
- Add records (with 0 case count) in periods where no cases were recorded.
- Recalculate cumulative figures.
- Data captured for specimens received in the 3 days before the reporting date is excluded due as cases reporting is likely incomplete.
2.3 Adjustments for Public Holidays
Public holidays tend to have lower number of cases received and results in distortions of the estimation of the reproduction number over time. Below we attempt to adjust for these discrepencies.
Public holiday dates are obtained from [5]
For each province counts of cases is then modelled as a function of:
- Week
- Day of Week
- Public Holiday
The impact of public holidays are then removed by observing the impact of public holidays in the model and reversing that out in the data. This has the effect of increasing the observed cases on public holidays and reducing them slightly on all other days. This effect is dependent on the province and day of the week.
3 Methodology
The methodology is described in detail here.
4 Results
4.1 Tests
Below raw numbers of test by specimen received date are plotted. A 7-day moving average is also plotted. No adjustment is made for public holidays for this data.
Tests
Tests for Last 30 Days
4.2 Test Positivity
Below raw test positivity by specimen received date is plotted. A 7-day sliding window test positivity rate is also plotted. No adjustment is made for public holidays for this data as both numerator and denominator should be impacted.
Test Positivity
Test Positivity for Last 30-days
4.3 Adjustments for Public Holidays to Cases
Cases before and after adjustment for public holidays for South Africa are shown below for March and April 2021. Cases are increased on days of public holidays and reduced on other days. Weekends are not impacted significantly.
Further in this report the adjusted cases are used.
Unadjusted and Adjusted Daily Cases for South Africa for March & April 2021
4.4 Cases
Below a 7-day moving average daily case count is plotted by province on a log scale since start of the epidemic:
Daily Cases by Province (7-day moving average)
Below the above chart is repeated for the last 30-days:
Daily Cases for Last 30-days by Province (7-day moving average)
4.5 Current \(R_{t,m}\) estimates by Province
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| province | Count (Week) | Week Ending | Reproduction Number [95% Confidence Interval] |
|---|---|---|---|
| Eastern Cape | 157 | 2021-04-19 | 0.8 [0.70 - 0.98] |
| Free State | 1,417 | 2021-04-19 | 1.2 [1.13 - 1.28] |
| Gauteng | 2,229 | 2021-04-19 | 1.0 [0.97 - 1.05] |
| KwaZulu-Natal | 528 | 2021-04-19 | 0.8 [0.76 - 0.91] |
| Limpopo | 150 | 2021-04-19 | 1.0 [0.83 - 1.14] |
| Mpumalanga | 744 | 2021-04-19 | 0.9 [0.87 - 1.01] |
| North West | 974 | 2021-04-19 | 1.1 [1.03 - 1.18] |
| Northern Cape | 897 | 2021-04-19 | 1.3 [1.19 - 1.43] |
| Western Cape | 907 | 2021-04-19 | 1.0 [0.91 - 1.04] |
| South Africa | 8,003 | 2021-04-19 | 1.0 [1.02 - 1.07] |
Estimated Effective Reproduction Number by Province
4.6 Maps of Effective Reproduction Number
Below estimates of the reproductive number are plotted on a map of South Africa [6].
Estimated Effective Reproduction Number Based on Cases by Province
4.7 Estimated Effective Reproduction Number for South Africa over Time
Below the results for South Africa over the last 90 days are plotted together with a plot since start of the pandemic.
Estimated Effective Reproduction Number Based on Cases for South Africa over last 90 days
Estimated Effective Reproduction Number Based on Cases for South Africa since 1 April 2020
4.8 Map of Effective Reproduction Number Over Last 60 Days
Below the reproduction number by week by province is animated:
4.9 Estimated Effective Reproduction Number for Provinces over Time
The results for each province over last 90 days are plotted below.
4.9.1 Eastern Cape
Estimated Effective Reproduction Number Based on Cases for Eastern Cape over Time
4.9.2 Free State
Estimated Effective Reproduction Number Based on Cases for Free State over Time
4.9.3 Gauteng
Estimated Effective Reproduction Number Based on Cases for Gauteng over Time
4.9.4 KwaZulu-Natal
Estimated Effective Reproduction Number Based on Cases for KwaZulu-Natal over Time
4.9.5 Limpopo
Estimated Effective Reproduction Number Based on Cases for Limpopo over Time
4.9.6 Mpumalanga
Estimated Effective Reproduction Number Based on Cases for Mpumalanga over Time
4.9.7 Northern Cape
Estimated Effective Reproduction Number Based on Cases for Northern Cape over Time
4.9.8 North West
Estimated Effective Reproduction Number Based on Cases for Gauteng over Time
4.9.9 Western Cape
Estimated Effective Reproduction Number Based on Cases for Western Cape over Time
4.10 Detailed Results
Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.
5 Discussion
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]:
- It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
- It relies on an assumed generation interval assumptions.
- The size of the time window can affect the volatility of results.
- Results are time lagged with regards to true infection.
- It’s sensitive to changes in case detection.
- The generation interval may change over time.
For example the the generation interval is based on international data and not South African data.
Further to the above the estimates are made under assumption that the cases are detected at a similar ratio to the underlying infections over time. Should this change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of case detection could result in an overestimating recent effective reproduction numbers. A more practical example may be a public holiday resulting in fewer specimens received on a particular day. Or, also, changes in testing, such as using more antigen tests (with lower sensitivity) relative to PCR tests could reduce the case ascertainment rate per test for example.
A relatively simple allowance is made for public holidays so as to avoid volatile figures due to public holidays. This allowance could be refined further but should result in a more consistent estimate of the reproduction number over time. Care should still be taken when reviewing results during periods where testing could be impacted.
Estimates for the reproduction number here are plotted in time period in which the specimen was received. Ideally we would wish to capture the date the infection occurred. These figures have not been shifted back, even approximately, to the date of infection.
Despite these limitation it is believed that the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.
6 Comparison with other estimates
In [7] similar estimate of the reproduction number are made. The main differences from those estimates are:
- The estimates [7] in are based on (estimated) date of symptom onset and should, in theory, be less susceptible to issues around testing (such as public holidays for example) than basing it on specimen received date. However, it may be difficult to obtain accurate symptom onset date.
- Similarly estimates are also made based on admissions and deaths in [7]. It’s very useful to look at estimates based on multiple end points, but in this case these require data sources not accessible to the public.
- The assumed generation interval assumptions are not exactly the same, but are reasonably similar.
References
[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133
[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim
[3] V. Marivate et al., “Coronavirus disease (COVID-19) case data - South Africa.” Zenodo, 21-Mar-2020 [Online]. Available: https://zenodo.org/record/3888499. [Accessed: 26-Oct-2020]
[4] National Institute for Communicable Diseases, “National COVID-19 Daily Report,” 2021 [Online]. Available: https://www.nicd.ac.za/diseases-a-z-index/covid-19/surveillance-reports/national-covid-19-daily-report/
[5] Republic of South Africa, “Public holidays in South Africa.” [Online]. Available: https://www.gov.za/about-sa/public-holidays. [Accessed: 15-Apr-2021]
[6] OCHA, “South africa - subnational administrative boundaries,” Dec. 2018 [Online]. Available: https://data.humdata.org/dataset/south-africa-admin-level-1-boundaries
[7] National Institute for Communicable Diseases, “The Daily COVID-19 Effective Reproductive Number (R) in South Africa,” Week 11 2020 [Online]. Available: https://www.nicd.ac.za/wp-content/uploads/2021/03/COVID-19-Effective-Reproductive-Number-in-South-Africa-week-11.pdf